A coronal funnel model, developed by D. Rabin, was tested against a calibrated spectroheliogram recorded in the 170-175 Å bandpass. This image was recorded on board a sounding-rocket experiment flown on 1994 November 3, called the Multi-Spectral Solar Telescope Array II (MSSTA II). MSSTA, a joint project of Stanford University, the NASA Marshall Space Flight Center, and the Lawrence Livermore National Laboratory, is an observing platform composed of a set of normal-incidence, multilayer-coated optics designed to obtain narrow-bandpass, high-resolution images (1 00 -3 00 ) at selected far-ultraviolet (FUV), extreme-ultraviolet (EUV), and soft X-ray wavelengths (44-1550 Å ). Using full-disk images centered at 1550 Å (C iv) and 173 Å (Fe ix/x), the funnel model, which is based on coronal back-heating, was tested against the data incorporating observed constraints on global coverage and measured flux. Found was a class of funnel models that could account for the quiescent, globally diffuse and unresolved emission seen in the 171-175 Å bandpass, where the funnels are assumed to be rooted in the C iv supergranular network. These models, when incorporated with the CHIANTI spectral code, suggest that this emission is mostly of upper transition region origin and primarily composed of Fe ix plasma. The funnels are found to have constrictions, À $ 6 20, which is in good agreement with the observations. Further, the fitted models simultaneously satisfy global areal constraints seen in both images; namely, that a global network of funnels must cover $70%-95% of the total solar surface area seen in the 171-175 Å image, and j45% of the disk area seen in the 1550 Å bandpass. These findings support the configuration of the EUV magnetic network as suggested by Reeves et al. and put forth in more detail by Gabriel. Furthermore, the models are in good agreement with differential emission measure estimates made of the transition region by J. C. Raymond & J. G. Doyle for temperatures 250;000 K T 650;000 K, based on full-disk observations made on board Skylab.